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The 2005 UK Workshop on Computational Intelligence 5-7 September 2005, London L2-SVM Based Fuzzy Classifier with Automatic Model Selection and Fuzzy Rule Ranking Shang-Ming Zhou and John Q. Gan Department of Computer Science, University of Essex, UK

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Background and Objectives(1/4) n The challenges : To apply SVM techniques to parsimonious fuzzy system modelling for regression and classification. Difficult to link the kernel functions in SVM to basis functions in fuzzy system. n Advantage of SVM: Parsimonious solutions based on quadratic programming

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Background and Objectives(2/4) n Chen and Wangs work [Chen and Wang 2003]: Established this sort of relation for fuzzy classification based on L1-SVM techniques. Parameters: kernel parameters and regularization parameter not updated optimally from data for fuzzy rule induction. n One objective : To apply L2-SVM techniques to fuzzy system modelling to optimally learn the parameters from data in terms of radius- margin bound J; Radius-margin bound: not hold in L1-SVM.

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L2-SVM based Fuzzy Classifier Construction (2/10) n Conditions of Applying SVM to Fuzzy Classifier Construction: are Mercer kernel; If are generated from a reference function through location shift, then are Mercer kernel [Chen and Wang 2003]; leading to Gaussian MFs; Kernel parameters manually selected in [Cheng and Wang 2003].

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L2-SVM based Fuzzy Classifier Construction (7/10) n Extraction Fuzzy Rules from L2-SVM Learning Results The number of fuzzy rules L is the number of support vectors; The premise parts of fuzzy rules: where is the jth element of the ith support vector. The consequent parts of fuzzy rules: where are the non-zero Lagrangian multipliers.

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L2-SVM based Fuzzy Classifier Construction (8/10) n Fuzzy rule ranking based on L2-SVM learning R-values of fuzzy rules: [Setnes and Babuska 2001] Absolute values of the diagonal elements of matrix R in the QR decomposition of firing strength matrix; -values of fuzzy rules: Determining the depth of the effect of the rule consequent. -values of fuzzy rules: Considering both rule base structure and effect of the rule consequent.

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L2-SVM based Fuzzy Classifier Construction (9/10) n Fuzzy rule selection procedure Evaluate the misclassification rates (MRs) of on the validation data set V and the test data set T separately: and ; Select the most influential fuzzy rules where is the threshold. Construct a fuzzy classifier by using the influential fuzzy rules selected.

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n To have applied L2-SVM to fuzzy rule induction for classification: Fuzzy rules optimally generated in term of radius-margin bound. Efficient way of avoiding the curse of dimensionality in high dimensional space. n Two novel indices for fuzzy rule ranking: Experimentally proved to be very effective in producing parsimonious fuzzy classifiers. Conclusions and Discussions(1/1)